Problem: Express this product in scientific notation: $(8.10\times 10^{3})\times (3.00\times 10^{2})$
Explanation: Start by collecting like terms together. $= (8.10\times 3.00) \times (10^{3}\times 10^{2})$ When multiplying exponents with the same base, add the powers together. $= 24.3 \times 10^{3\,+\,2}$ $= 24.3 \times 10^{5}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $24.3$ is the same as $2.430 \times 10$ $ = {2.430 \times 10} \times 10^{5} $ $= 2.430\times 10^{6}$